Honors Program

The L&S Honors Program serves over 1,300 students in the College of Letters & Science with an enriched undergraduate curriculum. Students in the program pursue the Honors in the Liberal Arts, Honors in the Major, or Comprehensive Honors Degrees. The program began in response to a 1958 petition by students seeking more challenging work and opportunities to "delve more deeply" into their fields of interest.

See below for Math Department specific information for completing an Honors in the Major distinction.

Honors in the Major: Mathematics Requirements

In order to earn the Honors degree in Math, in addition to completing the basic degree requirements, the student must

have a cumulative GPA of at least 3.3,

be in the Honors Program during the last three semesters before graduation,

honors candidates in Mathematics must complete the following basic math honors curriculum with grades B or better

Honors sections of 521-522

Honors sections of 541-542

At least two more courses in the 5XX or 6XX level (one of them usually 551) decided in consultation with the Honors advisor. They can be chosen from the list of optional courses below under “Course description”

The student needs to complete a capstone project consisting of writing a Senior Honors Thesis (681H-682H) or substitute a sequence of two upper-level courses deemed acceptable by the Mathematics Honors Advisor.

The following points should also be noted:

At least one of the two sequences 521-2, 541-2 must be completed by the end of the student junior year.

The student should declare his/her candidacy for the Honors Program in Mathematics to the Honors advisor by the start of the junior year. Please bring a copy of the L&S Honors in the Major Declaration Form.

Before choosing the Honors thesis option (681-2), the student must consult with the Honors advisor to prepare for and complete a suitable thesis. For up-to-date information about research groups for undergraduates within the math department please see "Senior Honors Thesis" below.

If the student elects to complete the alternative sequence of upper-level courses, the sequence must be approved by and permission to enroll given by the Honors advisor. Some past examples include 703-704, 714-715, 721-722, 721-725, and 741-742.

If you want information about the scheduled rotation of honors sections, the requirements to enroll in honors sections or for honors credits, and suggested plans for taking the scheduled honors sections, go to Honors in Calculus and other Honors sections below.

Honors in Calculus and Other Honors Sections

The mathematics department has in place a first class group of honors courses designated for the calculus sequences, linear algebra and differential equations.

Math 275-276 is the first group of courses in the sequence. They cover roughly the same material as Math 221-222 but with a much more in-depth approach to each subject, the emphasis placed on the understanding of the subject and the theoretical foundations. Following the same approach, Math 375-376 covers most topics on Math 234, the third calculus course, Math 340 linear algebra, plus many of the topics in a typical course in differential equations like for example Math 319. Math 275 and Math 375 are offered in the first semester only, while 276-376 are offered in Spring.

The initial placement in the sequence is by invitation but we also consider applications from qualified students who may not have received an invitation. Please contact one of the departmental Honors coordinators (Professors Street and Mari-Beffa in 2013/14) or the professor scheduled to teach the course.

The mathematics department also expects to offer honors sections or sections with honors credit available in the advanced undergraduate Math courses 341, 521, 522, 541, and 542. In the timetable the symbol "!" will denote a separate honors section and the symbol "%" will denote that honors credit is available in a regular section.

In addition, qualified students may enroll for Honors credit in 551, 552, 561, 567, 621, 623, 627, 629, 632, 641. Other higher level courses may occasionally appear in the timetable for honors credits (with the symbol !) or with honors credit available (with the symbol %). Regular sections can also be taken for Honors credits following the appropriate procedure described by the Letters and Science Honors program. Contact the Professor teaching the course if you need to do so. Any graduate course can be taken for Honors credit by a qualified undergraduate.

Course Descriptions

Below there is a list of descriptions of courses which are offered to students as part of the Honors curriculum. They are either mandatory or optional for an Honors student (see requirements above). For a complete list of math courses, please consult the undergraduate catalogue of the Mathematics department. For a description of graduate courses, please consult the graduate catalogue.

MATH 275-276 HONORS CALCULUS I-II

This sequence of five credit courses is the first part of the Calculus Honors sequence developed by the Math Department at the UW. The material covers essentially the same topics as the standard calculus I-II courses but the material is discussed in greater depth, and with much more emphasis on mathematical ideas. The goal of the sequence is to provide highly motivated and well prepared students with an opportunity to go beyond the traditional approach to the subject. The standard texbook is Calculus, V. I and II, by T.M. Apostol, and the prerequisites are a personal invitation or consent of the instructor.

MATH 375-376 HONORS CALCULUS III-IV

This sequence is the second part of five credit courses in the Calculus Honors sequence developed by the Math Department at the UW. The material covers essentially the same topics as the standard third semester calculus course, plus linear algebra in 375 and differential equations in 376. Again, the material is studied with more depth, more rigorously and with higher expectations of students. The standard texbook is Calculus, V. I and II, by T.M. Apostol, and the prerequisites are a personal invitation or consent of the instructor.

MATH 521-522 ANALYSIS I-II

This sequence of 3 credit courses (concluded by Math 621-Analysis III) introduces students to fundamental concepts and basic elementary theorems of analysis with emphasis on functions of several variables. The objective is to convey an understanding of the structure of analysis in itself as well as its role as a tool for other disciplines. This sequence is essential for students preparing for graduate studies in mathematics; also it should be taken by students of physics and engineering who intend to do graduate work in their areas.

Topics in 521: The real numbers, Elements of set theory and topological notions, metric spaces, Sequences and series, functions, limits, continuity, differentiation, integration, sequences and series of functions, uniform convergence.

Topics in 522: More on convergence (Fourier series, approximations of the identity, polynomial approximation, infinite products(, Compactness in metric spaces with applications, The contraction principle with applications, Differential calculus in normed spaces, implicit function theorem, and other topics.

Possible texts for Math 521-522: Principles of Mathematical Analysis, 3rd edition, by W. Rudin. Mathematical Analysis, by A. Browder. The way of analysis, by R. Strichartz.

MATH 541-542 MODERN ALGEBRA I-II

This is a sequence of 3 credit courses. Math 541 gives an introduction to basic abstract algebra. The coninuation emphasizes linear algebra and field theory. Both courses are essential for students preparing for graduate studies in mathematics.

MATH 551 ELEMENTARY TOPOLOGY

This 3 credit course is an introduction to the basic ideas and methods of point set topology. It is a good background for analysis courses and graduate topology courses. Topics: basic intuitive set theory, topological spaces, separation axioms, compactness, connectedness, metric spaces, special topics.

MATH 561 DIFFERENTIAL GEOMETRY

In this 3 cr. course, curves and surfaces in three and higher dimensional spaces are studied using calculus. The course is useful in preparation for the study of differentiable manifolds and for some aspects of applied mathematics and physics. Topics: curves, ac arc length, Serret-Frenet equations, two dimensional surfaces, first and second fundamental forms, geodesics, Gauss-Bonnet theorem.

MATH 623 COMPLEX ANALYSIS

This is a 3 credit introduction to the theory of analytic functions of a complex variable. Attention is given to the techniques of complex analysis as well as the theory. It is suitable for math majors as well as students in the physical sciences and engineering. Topics: complex numbers, elementary functions, analyticity, complex integration, Cauchy's theorem and formula, power series, residues, conformal mapping, harmonic functions.

Possible texts: Complex Analysis by E.M. Stein and R. Shakarchi.

Prereq: Math 321 or 521.

MATH 627 FOURIER ANALYSIS

This is a 3 credit introductory course in Fourier Analysis which is occasionally taught. It is targeted towards advanced students and should be useful especially for those students who plan to enter graduate studies in mathematics, physics and engineering.

Topics include: Motivation from PDE, Extensive study of Fourier series and their convergence. The Fourier transform on the real line and in Euclidean space. The discrete Fourier transform. More optional topics such as applications to number theory problems.

MATH 629 INTRODUCTION TO MEASURE AND INTEGRATION

This is a 3 credit introduction to measure and integration theory. It is particularly suitable for further studies in analysis, probability or statistics. Topics: Lebesgue integration, convergence theorems, general measure theory, differentiation, applications to probability.

Possible texts: Real Analysis by Royden; Real Analysis and Probability by Ash; Measure and Integral by Wheeden and Zygmund.

Possible texts: The Theory for Error-Correcting Codes I by N.J.A. Sloane and F. J. MacWilliams; The Theory of Information and Coding by R. McEliece (only the second part); Introduction to Error Correcting Codes by V. Pless.

Prereq: Math 320 or 340 or equiv., and 541 or consent of instructor.

Senior Honors Thesis and Undergraduate Research

MATH 681-682 SENIOR HONORS THESIS

This course is used for work on the honors thesis under the supervision of a faculty member.

Prereq: senior standing and enrollment in the math honors program.

If you are interested in participating actively in research activities, please talk to the Professor running a current program or consult with the Honors advisor (Prof. Brian Street in the academic year 2014/15).

Grants, Awards, etc.

Check out the list of Scholarships offered by the University of Wisconsin-Madison for undergraduate math majors.

In addition to these UW awards there are several federal and international competitions. Please consult with the Honors advisor for an up-to-date list.